This invention relates to telecommunications and more particularly a method and apparatus for optimizing the sampling phase in a PCM modem system.
In order to transmit high-speed data in the upstream direction of a Public Switched Telephone Network, PSTN, using an ITU-V. 92 like PCM modem connection it is necessary for a pre-equalizer to be employed by the analog modem transmitter to compensate for local loop channel distortion. It is known that the fractional sampling phase offset of the received symbol stream relative to the A/D quantizer at the central office, or CO, can have a significant effect on the performance of a pre-equalizer when the sampling rate is below the Nyquist rate. The effect can be large for symbol spaced pre-equalizers operating on received analog signals with significant excess bandwidth. Because the network sampling rate is fixed at 8 kHz, a digital modem operating on the network employing a PCM upstream modulation scheme would fall into this category.
For any particular equalization method and modulation scheme employed, it can be determined, either through experimentation or analysis, which fractional symbol phase offset at the analog modem will yield the best performance. Since the initial phase of the received signal is determined by the random call timing of the analog modem and the loop channel, it is desirable for digital modem to have the ability to adjust the sampling phase of its quantizer relative to the received signal.
However, the codec to which the digital modem is connected is remote from the digital modem and is not under its control. It is thus not possible for the digital modem to adjust the sampling phase of the upstream quantizer at the codec. It is therefore necessary to have a method by which the digital modem can direct the analog modem to adjust the phase of its transmitted signal such that it hits the codec at the optimum instant.
By way of further background, in the case of a typical PCM modem system there is an analog modem coupled over an analog link to a central office or CO, at which the analog signals are quantized and coupled to a digital modem. In the analog modem, a digital-to-analog converter is utilized to convert an incoming digital data stream to be transformed into an analog signal which is coupled via a hybrid circuit to a local analog loop. A node of the local analog loop is coupled to a central office which includes a codec and more importantly, a quantizer having both an analog-to-digital converter and a digital-to-analog converter, with these converters being utilized to connect the digital network to the analog loop.
As described in a paper by J. E. Mazo, entitled Optimum Timing Phase for an Infinite Equalizer, The Bell System Technical Journal, vol. 54, no. 1, January 1975, a system is described for optimizing the phase of a digital data stream or transmission, in which the phase refers to the phase of the samples. In this early paper, a digital equalizer is utilized to combine a sequence of the samples of the received data wave, with the equalizer being utilized to mitigate the effects of intersymbol interference and noise.
From this early work by J. E. Mazo, the phase of the sample point referenced to the sampling interval is adjusted at the receiver by adjusting the phase of the clock at the receiver which drives the analog-to-digital converter used to convert an incoming analog stream into a digital equivalent. As described in this paper, a different phase for the sampling point yields different performances for the communications system. J. E. Mazo describes how to find the optimal sampling phase and calculates the optimal sampling phase by looking at the entire frequency spectrum.
While such an optimization technique is useful when one has control of the analog-to-digital converter at the receiver, and more importantly the clock driving the A/D converter, in a PCM modem system the analog-to-digital converter is located at the central office or CO. It will be appreciated that the CO is quite far removed from the digital modem, which is the ultimate termination point for the transmission from the analog-to-digital converter. There is thus no ability to be able to remotely set the clock frequency and phase of the clock at the CO, thereby precluding the opportunity to utilize the J. E. Mazo optimization system for optimizing channel performance.
What will be apparent is that there is a requirement in PCM modem systems to be able either to adjust the frequency and phase of the clock at the CO in order to improve performance, or to be able to adjust the sampling phase at the analog modem to be able to optimize the system for channel interference and noise.
In the subject system a method is provided which allows a digital modem, during the initial training sequence, to adjust the sampling phase at the analog modem. This improves the performance of the pre-equalizer employed during data mode, which translates into lower error rates, and/or higher connect speeds.
Generally, this method can be described in the following steps. First, it is necessary for the analog modem to employ some sort of loop-back timing to lock its transmitter frequency to the network clock. After this frequency lock has been established, the digital modem can use the received quantized samples of a known dual phase analog probing signal transmitted by the analog modem to compute a phase estimate. This estimate is then compared to an optimum value and a sampling phase delay is computed which when employed at the analog modem shifts the fractional sampling phase offset to the optimum value at the CO. Note that this phase delay need only take on values between (0,1) with units of 1 symbol baud ({fraction (1/8000)} sec).
The digital modem encodes the required delay in the same manner it transmits other parameters to the analog modem during training. After transmission of the required delay by the digital modem and decoding of this delay by the analog modem, the analog modem delays the input data stream by the required delay. This can be accomplished through a hardware adjustment of its codec or through software methods such as interpolation. After this adjustment, the received analog signal will hit the network codec at the central office at the phase desired by the digital modem.
Since it is necessary for the analog modem to employ some sort of loop-back timing based on the network clock, a system such as described in U.S. Pat. No. 5,199,046 by F. Ling may be used. This phase adjustment will be maintained through the entire connection. How the appropriate delay is generated is now described.
While it is desirable to be able to adjust the phase and frequency of the clock which drives the digital-to-analog converter at the analog modem, in a preferred embodiment phase delay is accomplished by an interpolation of the digital data stream ahead of the digital-to-analog converter.
What sampling phase adjustment should be employed by the interpolation requires some detection of the communications channel. In the subject invention, the optimal sampling phase delay is determined at the digital modem through the utilization of the dual phase probing signal which is transmitted from the analog modem to the digital modem. The phase difference between the two phases of the 4 kHz probing signal is set, in one embodiment, to xcfx80/2, which corresponds to xc2xd with units of 1 symbol baud ({fraction (1/8000)} sec). Thus the second transmitted phase xcfx862, is determined by subtracting xcfx80/2 from the first transmitted phase, xcfx861. This relationship between the phases is maintained at the receiver. Therefore, the second received phase xcfx86B at the digital modem is the same as subtracting xcfx80/2 from the first received phase, xcfx86A.
At the receiver, xcfx86A is derived as the arctan of the summation of a ratio of the received signal with the first phase to the received signal with the second phase, e.g.       φ    A    =      arctan    ⁢          xe2x80x83        ⁢          1      /      N        ⁢          xe2x80x83        ⁢          ∑              xe2x80x83            ⁢                        -                      S1            ⁢                          (              n              )                                                            S            2                    ⁡                      (            n            )                              
Note that the above equation is valid when the sampling clock is twice the probing tone and the phase difference is xcfx80/2.
In operation, the probing signal is sent in two segments, the first with the first phase and the second with the second phase. The received signal with both phases are collected and used by the phase detector to detect xcfx86A. The first and second segments of the probing signal in one embodiment are sampled at the 8 kHz network clock rate.
With the sampling rate being 8 kHz, the probing signal in one embodiment is set to 4 kHz. The received phase at the codec of the probing signal xcfx86A is detected at the digital modem and the optimal sampling phase is calculated. The optimal sampling phase is that which results in a fractional sampling phase offset of zero or xcfx80 at the CO. This results in a maximum amplitude of the 4 kHz tone and thus optimum performance of the system.
Thus in one embodiment, the analog modem transmitter first sends a 4 kHz tone with phase xcfx861 followed by a second transmission with phase xcfx862, where xcfx862=xcfx861xe2x88x92xcfx80/2.
The reason why the 4 kHz tone is so important is that at the receive side, or more importantly at the CO, due to the analog-to-digital converter whose sampling frequency is below Nyquist rate, the digital signal is an aliased version of the original signal.
After the analog-to-digital converter, the components or portions of the signal due to the skirts of adjacent waveforms, P1 and P2, can either add or subtract depending on the phase of the fractional sampling phase offset, and this effect is called aliasing. One achieves better performance if these two components add. By making P1 and P2 add each other constructively at 4 kHz, it is more likely P1 and P2 will add each to the other at other frequencies. The important point is to select the optimal phase offset at which these two components, P1 and P2, add.
As will be seen, by selecting the probing signal frequency to be 4 kHz and setting the phase difference of the phases of the two tone segments to be xcfx80/2, it will be shown that the ratio of the received signal with the first phase to the received signal with the second phase yields the appropriate delay to be inserted at the analog end. In one embodiment,       φ    A    =      arctan    ⁢          xe2x80x83        ⁢                  -                  S1          ⁢                      (            n            )                                                S          2                ⁡                  (          n          )                    
Since, S1(n)=Acos(xcfx80n+xcfx86A)=A(xe2x88x921)n cosxcfx86A and S2(n)=Acos(xcfx80n+xcfx86B)=xe2x88x92A(xe2x88x921)n sinxcfx86A. To make the estimate more accurate, the ratio of s(n)s can be averaged over many samples, and this yields,       φ    A    =      arctan    ⁢          xe2x80x83        ⁢          1      /      N        ⁢          xe2x80x83        ⁢          ∑              xe2x80x83            ⁢                        -                      S1            ⁢                          (              n              )                                                            S            2                    ⁡                      (            n            )                              
where N is the number of received signal samples used to estimate phase xcfx86A.
From the detection of xcfx86A at the digital modem, one can calculate the optimal delay that the analog modem must insert to make the new phase of the received signal zero or xcfx80, which is optimal. By inserting the appropriate delay, one sets the sampling phase at the analog side such that the two components P1 and P2 add as opposed to subtract, which in turn yields optimal performance. From the above equations, and assuming the transmitter is currently transmitting at the xcfx862 phase, it can be shown that, the optimal delay D=(2xcfx80xe2x88x92xcfx86B)/(2xcfx80) mod 1==(2xcfx80+/2xe2x88x92xcfx86A)/(2xcfx80)mod 1.
In summary, in a PCM modem system, a method and apparatus for optimizing the fractional sampling phase offset to maximize the upstream data rate utilizes a probing signal from the analog modem generated during startup and having two or more distinct phases, with the probing signal being detected at the digital modem where an optimum sampling phase is calculated. Thereafter an optimal delay is calculated and is transmitted back to the analog modem where incoming data symbols are delayed by this amount. This makes the fractional sampling phase offset to be optimal at the central office quantizer.
More particularly, during startup the optimal sampling phase is determined by transmitting a probing signal having two different phases of a known phase difference and determining from the ratio of the two received signals the optimal sampling phase. The optimal sampling phase delay in one embodiment is the arctan of the ratio of the two received probing signal segments. The arctan is calculated from measuring the received segments and is utilized to specify the optimal sampling phase delay correction to be transmitted back to the analog modem.
Utilization of the two-phase 4 kHz tone permits one to assure that the components at the sampling point will be additive given the insertion of the correct sampling phase delay. Since additive, the calculated sampling phase delay, when applied at the analog modem, will make the fractional sampling phase offset optimal when the transmitted signals arrive at the central office. This yields a maximum amplitude of the 4 kHz tone, thus indicating that the system has been set for optimal performance.